How to import a rig and animation from maya?
In past year we used Maya for aditional effects on characters (especially for cloth simulations) and we discovered that the best way to import is .mdd.

This format transfers the maya animation and convert it into animated shapes keys:


Get your first pose (in maya) and export as .obj object
Export the animation from maya as .mdd
Import the .obj object in blender 
Select your object and import the animation as .mdd


Always check "keep vertex orders".